Humor affects our culture, our sociology, and our theology. If there are aliens without humor -- how would that affect their biological, psychological, theological and societal realities?
Again, some would say we can't even begin to speculate on that. But I think that is not true. Our minds are wonderfully capable of thinking out of the box, and sometimes way way out of the box. Think quantum mechanics, relativity, and string theory.
But also, again, patterns exist in this universe. Universal patterns exist in this universe. Biology, chemistry, physics, and mathematics all follow universal, repeatable patterns. I think we can apply logic to the question of alien biological, psychological, theological and societal realities. True, we don't have all the facts, but since when has that ever stopped humanity from speculating (and from such speculations, gaining ever new knowledge - some of it even useful!).
So, back to the question of humor. One approach to this is to try to examine why we humans have humor. For it seems to me most creatures on this planet do not have humor. Do paramecium laugh, chuckling at some amoeba joke? Most likely not - their awareness is too limited, their ability to notice incongruities also very limited. They can learn, so they can recognize on some very simple level some patterns. But humor? I'd be surprised.
But even more developed creatures do not have humor. Even highly organized social creatures do not have humor. Ants, who live rather short life spans, are too busy working building, maintaining, feeding, and protecting the colony.
But for even higher level creatures, some beginnings of humor seem to be there. Humor in play, for one: wild dolphins seem to show playful behavior, jumping into the air for the sheer pleasure of it. Many mammal young play with each other - though this play is a way to learn. And some of the play is quasi-aggressive behavior: learning how to fight. And some playful behavior is just plain mean: I've seen cats sneak up on each other, startling the one being snuck up upon. They definitely seem to like to tease the one cat in the group that has that Queenly attitude.
Seems, then, with due respect to Dr. Steven M. Sultanoff, it seems that humor is not just from recognizing incongruity in patterns, dealing with memories of a crisis, the joy of understanding something we at first misunderstood (which is related to the incongruity on a level), or experiencing the forbidden. It seems humor aids in learning, but also can be mean-spirited. It seems that humor is involved in dealing with complex, constantly changing social interactions.
Biologically, humor seems to be related to spindle neurons, which humans and apes both have, and which seemed to have evolved into being over a 15 million year span (so our most ancient ancestors probably didn't have that much of a sense of humor). However, spindle neurons have also been found in the great whales.
As creatures advance in their level of sentience, the more humor there seems to be. But, is it still absolutely necessary? Can other high level sentient beings be able to deal with complex, constantly changing social interactions without developing their equivalent to the spindle neuron. Just because humans (and to some extent apes and maybe even whales) developed a sense of humor doesn't mean that it is truly evolutionarily advantageous or useful. It could be something that has developed that just has a neutral effect on the ability of humans to survive and keep on evolving. In other words, if we never developed humor, maybe it would not have mattered.
But it does give one pause. Like the development of art. Seems the Neanderthal never developed a true artistic sense, but Cro-magnon eventually did, and when they did, humans were no longer the same. I think that humor is like art - it is the side-effect of being able to deal with complex abstract ideas, especially very complex and very abstract ideas. An intelligent alien species will have to find a way to deal with such complex abstractions as well.
Butovskaya, Marina L. and Alexander G. Kozintsev. "A Neglected Form of Quasi-Aggression in Apes: Possible Relevance for the Origins of Humor." Current Anthropology, Vol. 37, No. 4 (Aug. - Oct., 1996), pp. 716-717
Esther A. Nimchinsky et al. "A neuronal morphologic type unique to humans and great apes." Proc. Nat. Acad. Sci. USA, Vol. 96, pp 5268-5273, April 1999. (Can be found at http://www.pnas.org/cgi/reprint/96/9/5268.pdf).
Watson, KK, BJ Matthews, and JM Allman. "Brain activation during sight gags and language-dependent humor". Cereb Cortex 17 (2): 314–24. (2007)